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Interaction of Vortex Filaments -Towards a Deeper Understanding of Vortex Dynamics-

Research Project

Project/Area Number 20K14348
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionTokyo University of Science

Principal Investigator

Aiki Masashi  東京理科大学, 創域理工学部数理科学科, 講師 (90734400)

Project Period (FY) 2020-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Keywords渦糸 / 非線形偏微分方程式 / 数学解析 / 安定性 / 渦輪 / 局所誘導方程式 / 安定性解析 / カオス / 衝突 / 通り抜け / 翼端渦
Outline of Research at the Start

航空機の翼の端から発生する翼端渦や渦輪など,我々の身の回りには渦を伴う様々な流体(空気など)の運動が存在し,これら現象を流体の基本理論に基づいた定式化によって解明することは学術的な価値だけでなく工学的な応用においても大変有用である.しかし,翼端渦など,複数の細い渦構造の相互作用を数学的に扱う試みは少ない.そこで本研究では,「翼端渦」と「渦輪の追い越し」の二つの現象を数学的に定式化および解析することによってこれら現象をより深く理解するための研究を行う.特に,翼端渦の研究においては航空機の翼の設計など工学的な応用を行うための基礎理論を構築することも目的とする.

Outline of Final Research Achievements

The aim of this research project is to mathematically formulate and analyze the interaction of thin vortex structures within fluids. Specifically, we utilize nonlinear partial differential equations describing the motion of vortex filaments and investigate the existence and stability of solutions which correspond to particular motion patterns. In this regard, we were able to publish 2 research papers (1 accepted, 1 submitted). Furthermore, we investigated the motion pattern of three coaxial circular vortex filaments and obtained numerical evidence which suggests the existence of interesting motion patterns.

Academic Significance and Societal Importance of the Research Achievements

流体における渦運動は,流体の運動を構成する重要な要素の1つであり,渦運動の詳細を数学的に解析することは,流体の運動を理解するための基礎理論を構築することに資するものである.また,細い渦構造の相互作用は航空機の翼端渦などにも表れる.これら渦の挙動や安定性を数学的に解析することによって翼端渦の影響を軽減し,航空機の飛行を効率化するための基礎理論を構築することにつながる.

Report

(5 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (7 results)

All 2023 2021 2020

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (6 results) (of which Int'l Joint Research: 5 results,  Invited: 6 results)

  • [Journal Article] The Hasimoto Transformation for a Finite Length Vortex Filament and its Application2023

    • Author(s)
      相木雅次
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 55 Issue: 6 Pages: 72737295-72737295

    • DOI

      10.1137/22m1524424

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Presentation] The Hasimoto Transformation for a Finite Length Vortex Filament and its Application2023

    • Author(s)
      相木雅次
    • Organizer
      RIMS Workshop on Mathematical Analysis in Fluid and Gas Dynamics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Interaction of a Pair of Coaxial Circular Vortex Filaments2023

    • Author(s)
      相木雅次
    • Organizer
      The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Hasimoto Transform for a Finite Length Vortex Filament and its Application2023

    • Author(s)
      Masashi Aiki
    • Organizer
      The 40th Kyushu Symposium on Partial Differential Equations
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Head-on Collision of Coaxial Vortex Rings2021

    • Author(s)
      相木雅次
    • Organizer
      Quasi-linear PDEs in fluids
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Interaction of a Pair of Coaxial Circular Vortex Filament2020

    • Author(s)
      相木雅次
    • Organizer
      2020年度 第1回明治非線型数理セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] On the head-on collision of coaxial vortex rings2020

    • Author(s)
      相木雅次
    • Organizer
      Mathematical Analysis of Viscous Incompressible Fluid
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2020-04-28   Modified: 2025-01-30  

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